A Fast Method for Correlated Updates of Proton PDFs and the Strong Coupling $α_s$

Abstract

We present an extended version of the \texttt{ePump} framework that enables the simultaneous profiling of proton parton distribution functions (PDFs) and the strong coupling $α_s$ using new experimental data. By promoting $α_s$ to a fit parameter within the Hessian updating formalism, the method performs coherent updates of $\{\text{PDFs},α_s\}$ while preserving parameter correlations and the full covariance structure. Validation studies based on CTEQ-TEA analyses with collider data demonstrate that the upgraded \texttt{ePump} accurately reproduces the shifts in PDFs, the preferred $α_s(m_Z)$, and the associated uncertainty reductions obtained in full global fits, including those inferred from Lagrange--Multiplier scans; small deviations arise only for data sets whose $χ^2$ profiles exhibit nonlinear behavior. Applications to representative collider measurements illustrate the impact on the gluon distribution and on precision observables such as the Higgs boson production cross section via gluon fusion. This enhanced framework provides a fast and reliable tool for assessing the effects of new data on the global QCD parameter space, offering near-global-fit accuracy at a fraction of the computational cost.

Figures (8)

• Figure 1: The scan of the strong coupling constant at the scale $M_Z$ for NNLO PDFs. Left: The baseline PDFs are obtained from the standard CT18 analysis but with the E268 data set (ATLAS 7 TeV $W/Z$, with an integrated luminosity of 35 pb$^{-1}$ collected in 2010 ref:E268) removed, and subsequently updated by ePump to include the missing E268 data. The $\chi^2$ values are computed using ePump. Right: The corresponding results obtained from the full CT18 analysis, using the CTEQ-TEA global analysis code.
• Figure 2: The scan of the strong coupling constant at the scale $M_Z$ for NNLO PDFs. Left: The baseline PDFs are obtained from the standard CT18A analysis but with the E248 data set (ATLAS 7 TeV $W/Z$ production with an integrated luminosity of 4.6 fb$^{-1}$ collected in 2011 ref:E248) removed, and subsequently updated by ePump to include the missing E248 data. The $\chi^2$ values are computed using ePump. Right: The corresponding results obtained from the full CT18A analysis, using the CTEQ-TEA global analysis code.
• Figure 3: The scan of the strong coupling constant at the scale $M_Z$ for NNLO PDFs. The baseline PDFs are obtained from the standard CT18A analysis but with the E248 data set (ATLAS 7 TeV $W/Z$ production with an integrated luminosity of 4.6 fb$^{-1}$ collected in 2011) removed, and subsequently updated by ePump to include the new E218, E553, and E554 data sets. The $\chi^2$ values are computed using ePump. The preference for a larger $\alpha_s(m_Z)$ is driven consistently by all three post-CT18 data sets: E218 (LHCb 13 TeV $y_Z$), E553 (ATLAS 8 TeV jet), and E554 (ATLAS 13 TeV jet).
• Figure 4: Comparison of the gluon PDF for three analyses. The first (CT18Am248) corresponds to the standard CT18A analysis with the E248 data set removed. The middle result is obtained by updating this baseline using ePump to include E248 and the new E553, E581, and E528 data sets. The bottom result is obtained by updating with the same new data sets, but with $\alpha_s(m_Z)$ simultaneously updated.
• Figure 5: LM scans for the gluon PDF at $Q = 125$ GeV and $x = 0.01$. Left: The PDF is based on the standard CT18A analysis with the E248 data set removed. Middle: The PDF is updated by ePump to include E248 (ATLAS 7 TeV $W/Z$) and the new E553 (ATLAS 8 TeV jet), E581 (CMS 13 TeV $m_{t {\bar{t}}}$), and E528 (CMS 13 TeV $y_{t {\bar{t}}}$) data sets. Right: The PDF is updated using the same new data sets, but with $\alpha_s$ updated simultaneously. All $\chi^2$ values are computed using ePump. The CMS 13 TeV top-quark pair production data sets, E581 and E528, consistently prefer an enhanced gluon PDF at small $x$ ($x=0.01$).